This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To show the graph, you would plot the Cost and Revenue functions on a coordinate plane. Step 1: Set up the axes. • The horizontal axis (x-axis) represents the Number of Bottles Produced and Sold. • The vertical axis (y-axis) represents Total Cost/Revenue (₦). Step 2: Plot the Cost Function C(x) = 10,000 + 0.03x. • This is a straight line. • Y-intercept (Fixed Cost): When x=0, C(0) = 10,000. Plot the point (0, 10,000). • Cost at Maximum Annual Capacity: When x=600,000, C(600,000) = 10,000 + 0.03 × 600,000 = 28,000. Plot the point (600,000, 28,000). • Draw a straight line connecting these two points. Step 3: Plot the Revenue Function R(x) = 0.46x. • This is also a straight line. • Origin: When x=0, R(0) = 0. Plot the point (0, 0). • Revenue at Maximum Annual Capacity: When x=600,000, R(600,000) = 0.46 × 600,000 = 276,000. Plot the point (600,000, 276,000). • Draw a straight line connecting these two points. Step 4: Identify the Break-Even Point. • The break-even point is where the Cost line and the Revenue line intersect. • From the previous calculation, the break-even point is approximately (23,256 bottles, ₦10,697.76). Mark this intersection point on your graph. Description of the Graph: You will see two straight lines originating from the y-axis. • The Cost line starts at ₦10,000 on the y-axis and slopes upwards. • The Revenue line starts at ₦0 (the origin) and slopes upwards more steeply than the cost line. • The point where these two lines cross is the break-even point. To the left of this point, the cost line is above the revenue line, indicating a loss. To the right of this point, the revenue line is above the cost line, indicating a profit.